Reference: Einstein’s 1920 Book
Section XXIII (Part 2)
Behaviour of Clocks and Measuring Rods on a Rotating Body of Reference
Please see Section XXIII at the link above.
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Summary
The physical interpretation of the space-time continuum in the context of the general theory of relativity may require some patience and power of abstraction. In a Galilean space-time continuum, only uniform motion is manifested. But in the general space-time continuum, inertia or consistency is also manifested due to curvilinear motion. This is taken as the effect of a gravitational field. The general law of gravitation would then be expected to explain not only the motion, but also the inertia/consistency of the stars.
In the given thought experiment, the reference point at the edge of the rotating disc will have much greater motion and flexibility than the reference point at the center of the disc. Therefore, measurements by clocks and rods will differ greatly at the two locations. As a result, the physical interpretation of the space-time continuum shall differ greatly in the gravitational field observed.
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Final Comments
The space-time continuum in the gravitational field of a rotating body of reference shall have a varying sense of inertia/consistency associated with different locations.
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